Question: Determine where $f(x)$ intersects the $x$ -axis. $f(x) = (x + 8)^2 - 1$
Answer: The function intersects the $x$ -axis where $f(x) = 0$ , so solve the equation: $ (x + 8)^2 - 1 = 0$ Add $1$ to both sides so we can start isolating $x$ on the left: $ (x + 8)^2 = 1$ Take the square root of both sides to get rid of the exponent. $ \sqrt{(x + 8)^2} = \pm \sqrt{1}$ Be sure to consider both positive and negative $1$ , since squaring either one results in $1$ $ x + 8 = \pm 1$ Subtract $8$ from both sides to isolate $x$ on the left: $ x = -8 \pm 1$ Add and subtract $1$ to find the two possible solutions: $ x = -7 \text{or} x = -9$